1. 150.00 g to dag 0.000 678 hm to dm 654 000 g to Mg 3200 cL to kL

2. Measuring Correctly

3. How to measure correctly
A measurement can only be as accurate as the measuring device.
Can you measure mm with this ruler?

4. How to measure correctly
Scientists must be consistent in their experimentation so their results can be repeated by anyone.

5. How to measure correctly
It is done using significant digits, also known as significant figures (sig figs).
Significant digits - a measurement consists of all digits known for certain, plus one final, estimated digit.

6. How to measure correctly
Think of significant digits, as “measured” digits.
This ensures that anyone using a particular measuring device will end up with the same measurement.

7. Let’s try it… 50 60

8. Let’s try it… 50 60

9. Let’s try it… 50 60

10. Let’s try it… 8 9

11. Let’s try it… 8 9

12. Let’s try it… 8 9

13. Let’s try it… 9 8

14. Let’s try it… 20 10

15. Let’s try it… 90 80

16. Review 90 80

17. Review 26 25

18. Review 20 30

19. Review 15 16

20. Review
100
200

21. Review
500
600

22. Review
3000
4000

23. Review
7000
8000

24. Significant Digits
What if you come upon a measurement that someone else has taken?
How many of the digits have been “measured” making them significant?

25. Significant Digits
There are 5 rules that govern when a number in a measurement is significant.
Recall: Think of a significant digit as being a “measured” digit.

26. Significant Digits
Digits other than zero are always significant.
Examples: 73 g
89.2 g
0.14 g

27. Significant Digits
One or more FINAL zeros used AFTER the decimal point are always significant.
Examples: m
97.10 cm g

28. Zeros between two significant digits are always significant.
Examples: g
801 m mg
The decimal point can fall between

29. Significant Digits
Zeros used solely for spacing the decimal point are not significant; the zeros are space holders only.
Examples: g m

30. Significant Digits
Counting numbers and conversion factors have an infinite number of SD’s.
A counting number does not come from a measurement and occur in an exact number.
Conversion factors are also exact numbers, therefore have an infinite number of SD’s.
Ex: 24 students, 1 m = 100 cm

31. Significant Digits
2007 m g
100 mg km cm
165 cars kg

32. Significant Digits
2007 m  4
g  4
100 mg  1
km  6
cm  1
165 cars  infinite or 
kg  3

33. Significant Digits m
0.050 g mg
960 houses cm
29.30 s kg

34. Significant Digits
m  2
0.050 g  2
mg  5
960 houses  infinite
cm  5
29.30 s  4
kg  1

35. Review
25.00 m
0.005 g mg
9700 houses cm kg

36. Review
25.00 m  4
0.005 g  1
mg  5
9700 houses  infinite
cm  4
kg  1

37. Significant Digits
Here is the trouble:
How can you express the measurement 7000 meters with 4 significant digits?

38. Significant Digits
There are 3 ways:
Write in the decimal point.
7000. meters

39. Significant Digits
Put a line over a zero to make that zero significant. You can only use one line!
7000 meters

40. Significant Digits
Use Scientific notation. This is the best and most useful method.
7.000 x 103 meters

41. Scientific Notation
Use scientific notation for very large or very small numbers that may be too cumbersome to write.
Examples:

42. Scientific Notation
General formula M x 10n
Where 1 M < 10 and n is a positive or negative whole number. (integer)
Examples:
5 x x 10-11

43. Scientific Notation
You must not forget your significant digits…
2000
2000.0

44. Scientific Notation
You must not forget your significant digits…
= 2 x 103
= x 103

45. Put these in correct Sci. Not.
2007 m g
100 mg km cm
165 cars kg

46. Answers
2007 m x 103
g x 10-3
100 mg 1 x 102
km x 102
cm 7 x 10-4
165 cars x 102
kg x 10-2

47. Put these in correct Sci. Not.m
0.050 g mg
960 houses cm
29.30 s kg

48. Answers
m 2.5 x 104
0.050 g 5.0 x 10-2
mg x 102
960 houses x 102
cm x 10-2
29.30 s x 101
kg 5 x 10-6

49. Review: Put these in correct Sci. Not.m
380 g mg m cm s kg

50. Answers
m x 103
380 g x 102
mg x 10-2
m 1 x 104
cm x 10-3
s x 104
kg x 10-1

51. SD’s and Math
Measurements used in calculations often contain different numbers of SD’s.
The answer must not have more SD’s than are justified by the original measurements, especially if calculators are used!
(Like those TI 80 millions!)

52. SD’s and Math
Your calculator is stupid.
You must make it smarter.

53. Example:
A block of wood is measured using a ruler. The dimensions are found to be: cm x 3.18 cm x cm
What is the volume of the block of wood in cm3?

54. Example:
The volume is equal to the three measurements multiplied.
V = l x w x h
29.25 cm x 3.18 cm x cm
V = cm3

55. Example:
V = cm3
This is not correct. Why not?
Your calculator is stupid!!!
1.28 x 103 cm3

56. The Rule
Multiplication/Division: the answer cannot have more SD’s than the number in the calculation with the fewest SD’s.
The answer should be rounded off to the same number of SD’s as in the measurement with the fewest SD.

57. The Rule
Addition/Subtraction: the answer should be rounded off so that the answer contains only as many decimal places as the measurement having the least number of decimal places.

58. + The Rule Example: 487.2 cm 5.684 cm 492.884 cm
rounded to 1 decimal place cm +

59. How many SD’s? Convert to meters, then put it in correct scientific notation.mm Mm
800.0 dm m cm

60. We Try!
2.48 x 2.8
46.75  600
3.758 – 1.25

61. You Try!
200 x 30.5
892.5  2.8
15.2 – 8.358

62. You Try!
200 x 30.5 =  6000 or x 103
892.5  2.8 =  320 or x 102
15.2 – =  6.8
=  82.6

63. You Try!
A block of wood is measured using a ruler. The dimensions are found to be: cm x cm x cm
What is the volume of the block of wood?

64. Answer
My calculator tells me the answer is cm3.
With correct SD’s, the answer is 1.56 x 103 cm3

65. You Try!
A student finds the mass of a metal cylinder to be 78.9 grams and the volume to be cm3. What is the density?

66. Answer
Density = =
= g/cm3
= 2.51 g/cm3
mass
78.9
volume
31.43

67. One more
Density = 2.51 g/cm3
What is your percent error if the correct density is 3.01 g/cm3? Pay attention to SD’s.

68. Answer
| |
3.01
| |
17 %
x 100
x 100 = %